There are two things that can help. First, make sure that the chown command looks like:

sudo chown -R mysql /usr/local/mysql/*

or if you are already in that directory, you can also try

sudo chown -R mysql .

Make sure you list the directory (ls -al /usr/local/mysql) to ensure the chown command actually worked.

For those who had trouble starting up the mysql daemon, first type "su", then enter your root password at the prompt. This will log you into the shell as root, and from that point on you don't need to type "sudo" to run a command that needs to run as root. Just make sure you exit the root session when you are done by typing "exit", otherwise every command afterwards will run with root priviledges, a good way to shoot yourself in the foot. At that point you can type "/usr/local/bin/mysql_safe --user=mysql &" and it should work as advertised.